Joint State and Disturbance Estimation Based on the Generalized Observer Form

A method for joint state and disturbance estimation is developed for discrete-time nonlinear reversible control systems. The observer is constructed in two steps. First, the state vector is extended to include also the disturbances. Under the assumption that the disturbances are constant, the extended state equations depend only on the extended state variables and input variables. Thus, a standard state observer can be constructed for the extended state equations. For this, in the second step one transforms the extended state equations into the generalized observer form for which an observer can be easily constructed. Since the extended state includes both the state variables and the disturbance variables, the observer will find the estimates of both. Finally, the developed method is applied to estimate the state and parameter values of type 1 diabetes model.